Given $ m \angle AOB = 5x + 5$, $ m \angle BOC = 7x + 41$, and $ m \angle AOC = 154$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {5x + 5} + {7x + 41} = {154}$ Combine like terms: $ 12x + 46 = 154$ Subtract $46$ from both sides: $ 12x = 108$ Divide both sides by $12$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 7({9}) + 41$ Simplify: $ {m\angle BOC = 63 + 41}$ So ${m\angle BOC = 104}$.